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2 years ago

14

The width of a rectangle is 4 units shorter than three-fourths the length; x. Write an expression that represents the perimeter

of the rectangle.

1 answer:

qaws [65]2 years ago

6 0

The expression that represents the perimeter of the rectangle is 4x² + 14x - 3 = 0

<h3>How to determine the expression</h3>

The formula for perimeter of a rectangle is given as;

Perimeter = 2 ( length + width)

Let the length of the rectangle be x

Width of the rectangle be y

From the information given, we have that;

y = 4 - 3/4x

Make into linear equation

y = 16x - 3 / 4x

Now, let's substitute the variables into the formula

Perimeter = 2 ( $\frac{16x -3 }{4x} + x$ )

Find the LCM of the bracket

Perimeter = $2(\frac{16x - 3 + 4x^2}{4x} )$

Perimeter = $\frac{4x^2 + 16x - 3}{2x}$

2x = 4x² + 16x - 3

Collect like terms

4x² + 16x - 2x - 3 = 0

4x² + 14x - 3 = 0

Thus, the expression that represents the perimeter of the rectangle is 4x² + 14x - 3 = 0

Learn more about a rectangle here:

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Hoochie [10]

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3 years ago

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The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative

madam [21]

The true statement is:

"The range of the function is all real numbers less than or equal to 9."

<h3>Which statements are true?</h3>

Here we have the quadratic function:

$f(x) = -x^2 - 4x + 5$

And we want to see which of the given statements are true.

The first one is:

"The domain is al real numbers less than or equal to -2"

This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).

The second statement is:

" The domain of the function is all real numbers less than or equal to 9."

Also false

Third one:

" The range of the function is all real numbers less than or equal to −2"

The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.

In this case, the quadratic function is:

$f(x) = -x^2 - 4x + 5$

So the vertex is at:

$x = 4/(2*-1) = -2\\$

Then the y-value of the vertex is:

$f(-2) = -(-2)^2 - 4*(-2) + 5 = -4 + 8 + 5 = 9$

So the range is the set of all real numbers less than or equal to 9.

So the above statement is false, and the final one:

"The range of the function is all real numbers less than or equal to 9."

Is the true statement.

If you want to learn more about quadratic functions:

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8 0

2 years ago

Suppose approximately 75% of all marketing personnel are extroverts, whereas about 55% of all computer programmers are introvert

irina [24]

Answer:

A.)

0.852 ; 0.999 ; 0.013

B.)

0.018 ; 0.593 ; 0.050

Step-by-step explanation:

Given :

Proportion of marketing personnel that are extrovert, p = 0.75

1 - p = 1 - 0.75 = 0.25

Proportion of computer programmers that are introverts, p = 0.55

1 - p = 1 - 0.55 = 0.45

According to binomial distribution formula :

P(x =x) = nCx * p^x * (1 - p)^(n - r)

A.) n = 15

Probability that 10 or more are extrovert

P(x ≥ 10) = p(x = 10) + p(x = 11) +... p(x = 15)

To save computation time, we can use a binomial probability calculator ;

P(x ≥ 10) = 0.8516 = 0.852

Probability that 5 or more are extrovert :

P(x ≥ 5) = p(x = 5) + p(x = 6) +... p(x = 15)

To save computation time, we can use a binomial probability calculator ;

P(x ≥ 5) = 0.9999 = 0.999

Probability that all are extrovert :

P(x = 15) = 15C15 * 0.75^15 * 0.25^0

P(x = 15) = 1 * 0.75^15 * 0.25^0

P(x = 15) = 0.01336 = 0.013

B.

What is the probability that all are introverts?

n = 5

None are introvert :

P(x = 0) = 5C0 * 0.55^0 * 0.45^5

P(x = 0) = 1 * 1 * 0.0184528125

P(x = 0) = 0.01845 = 0.018

P(x ≥ 3) = p(3) + p(4) + p(5)

To save computation time, we can use a binomial probability calculator ;

P(x ≥ 3) = 0.5931 = 0.593

Probability that all are introvert

P(x = 5) = 5C5 * 0.55^5 * 0.45^0

P(x = 5) = 1 * 0.55^5 * 0.45^0

P(x = 5) = 0.0503 = 0.050

6 0

3 years ago

Help plz find the equation

tatiyna

Question # 1

Step-by-step Explanation:

Given

$\frac{1}{2}\div \frac{2}{3}$

solving

$\frac{1}{2}\div \frac{2}{3}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

$=\frac{1}{2}\times \frac{3}{2}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}$

$=\frac{1\times \:3}{2\times \:2}$

$\mathrm{Multiply\:the\:numbers:}\:1\times \:3=3$

$=\frac{3}{2\times \:2}$

$\mathrm{Multiply\:the\:numbers:}\:2\times \:2=4$

$=\frac{3}{4}$

Therefore, completing the blanks:

$\frac{1}{2}\div \frac{2}{3}=\frac{1}{2}\times \frac{3}{2}=\frac{3}{4}$

Question # 3

Step-by-step Explanation:

Given

$\frac{2}{5}\div \frac{3}{4}$

solving

$\frac{2}{5}\div \frac{3}{4}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

$=\frac{2}{5}\times \frac{4}{3}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}$

$=\frac{2\times \:4}{5\times \:3}$

$\mathrm{Multiply\:the\:numbers:}\:2\times \:4=8$

$=\frac{8}{5\times \:3}$

$\mathrm{Multiply\:the\:numbers:}\:5\times \:3=15$

$=\frac{8}{15}$

Therefore, completing the blanks:

$\frac{2}{5}\div \frac{3}{4}=\frac{2}{5}\times \:\frac{4}{3}=\frac{8}{15}$

Question # 5

Step-by-step Explanation:

Given

$\frac{3}{4}\div \frac{5}{7}$

solving

$\frac{3}{4}\div \frac{5}{7}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

$=\frac{3}{4}\times \frac{7}{5}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}$

$=\frac{3\times \:7}{4\times \:5}$

$\mathrm{Multiply\:the\:numbers:}\:3\times \:7=21$

$=\frac{21}{4\times \:5}$

$\mathrm{Multiply\:the\:numbers:}\:4\times \:5=20$

$=\frac{21}{20}$

Therefore, completing the blanks:

$\frac{3}{4}\div \frac{5}{7}=\frac{3}{4}\times \:\frac{7}{5}=\frac{21}{20}$

6 0

3 years ago

Simplify the expression 7v + 2w-12v

ladessa [460]

<span>7v + 2w-12v</span>

= 7v-12v+2w
= 5v+2w

Nothing else we can to to this

5 0

4 years ago

Read 2 more answers